The TeamCity plugin does not have a concept of object mappings and currently does not support the use of migration scripts.
The best work around for this is to use SQL Compare to handle the rename.
If you open SQL Compare and set the source to be either source control and then point at the repository or database (if it is up to date). Then set the target as the database which you are trying to upgrade.
On the Table Mapping tab find the table where you renamed the column, click on the status field for that row and then map up the old and new columns appropriately.
When you are happy with the mappings, click Compare Now on the Edit project dialog.
You will then need to select the changes you want to deploy and click on the Deployment Wizard and follow the instructions. You could just deploy the column rename in this manner.

Because the old column name is included in a package that is currently deployed. You will then need to turn off generate upgrade script in the TeamCity plugin and run a build and deploy the new package to all the environments where you had to update the column name using SQL Compare.
You can then turn on the Generate upgrade script option back on.